Damage in a comprehensive model for shape memory alloys in logarithmic strain space

Abstract

Shape memory alloys (SMAs) possess considerable complexity in response to thermomechanical load due to their strong dependence on strain, stress, temperature and history. This high complexity is a limiting factor in the fatigue analysis of SMA structures. With this in mind, a comprehensive phenomenological model is developed to address nearly all of the features in SMAs with a particular focus on the development of damage. Due to the fact that many SMA structures experience large deformations, the model is developed in finite strains using the logarithmic strain space approach. Besides the balance of linear momentum, the model includes the heat conduction equation and two micromorphic nonlocal balance laws. The latter are introduced to regularize the softening associated with the damage and transformation. The material model incorporates a damage evolution law that depends on the integration of a simplified dissipation term. The model is applied to a few examples to observe the interaction of the features and to illustrate the applicability of the model for rupture and fatigue analysis. The interaction of the features is shown to produce a reasonable representation of the cyclic loading of wires at different loading rates. Rupture is shown to occur due to a large amount of plastic strain and can be performed due to the nonlocal approach for the damage. The fatigue analysis shows some promising accuracy but only if the dissipated area is captured properly.